Refractor optical system

ABSTRACT

A refractor optical system having a new series of spherical and cylinder lenses substantially eliminates the irregular occurrence of additive errors when lenses spaced from the reference plane are used or more than two lenses are combined and permits correction for the significant additive errors by non-additive lens selection is disclosed.

BACKGROUND OF THE INVENTION

This is a continuation-in-part of application Ser. No. 894,455, filedApr. 7, 1978, now U.S. Pat. No. 4,215,919.

This invention relates to refractor optical systems and, moreparticularly, to a spherical and a cylinderical lens series for arefractor having regular additive errors to permit non-additivecombinations for correction of additive error.

Refractors are well known ophthalmic instruments used for determiningthe proper lens value necessary to correct the defective vision of apatient. The refractor typically includes a right hand battery and aleft hand battery, each for enabling the practitioner to place variouscorrective lenses in alignment with a respective patient's eye. Each ofthe batteries is alike and each includes a series of spherical lensesand series of cylindrical lenses. The spherical lens assembly and thecylindrical lens assembly each conventionally include a pair of discs.One of each pair of discs contains lenses having a "weak" power inincremental increases of power and the other disc of each pair containslenses having "strong" power. The lenses of the "strong" power disc areof sequentially increasing power with the increments of increasing powerusually at least being equal to the highest power of the corresponding"weak" lens plus the "weak" lens increment. The practitioner may rotateone of the lenses in each disc into alignment with the patient's eye. Inearly refractors, like trial lens sets, the practitioner could selectthe particular combination of lenses which he wished to place before thepatient's eyes. Each lens was manufactured to have a specific powerwhether the lens was used by itself or in combination with one or moreother lenses. For example, to provide a cylinder power of plus 6.50diopters, the practitioner would select the +6.0 diopter sphere lens andthe +0.5 diopter cylinder lens. In lens series of such prior artdevices, the designer attempted to minimize the error in any particularcombination since each lens, for example, the +0.25 diopter cylinderlens, was used any time the practitioner needed to add 0.25 diopter ofcylinder. In the average trial lens sets, there are over three thousandlens combinations in which the 0.25 diopter cylinder lens may be used.Since the only way to correct for additive error was to refer to areference chart which covered all the permutations of lens combinations,the lens designer attempted to minimize the error resulting fromcombining lenses in each possible combination of the series.

As used hereinafter, the term "additive error" refers to the differencebetween the real cylinder power of a lens combination and the powerexpected from the sum of the powers of the individual cylinder lenses inthe combination. The term "significant" additive error is used herein todenote additive error in excess of 0.1 diopter.

As refractors developed and became more refined, the disc containing the"weak" lenses were mechanically coupled to the disc containing the"strong" lenses. This permitted the practitioner to operate a singlecontrol to vary the spherical power presented to the eye and similarly asingle control to vary the cylinder power presented to the eye. Theconstrictions placed upon lens design were even more severe in suchinstruments because the mechanical linkage used to couple the cylinderlens discs prevents the practitioner from personally selectingindividual lens combinations.

PRIOR ART

U.S. Pat. No. 1,455,457, issued May 15, 1923 to Tillyer, discloses a"new" series of test lenses which minimizes additive error when morethan one lens is used. This patent describes the defects of the priorart and teaches that the minimization of the amount of error whencombining lenses is important. The lens series is not designecd toprovide the least number of errors or predictable combinations whichhave significant error.

U.S. Pat. No. 2,266,797, issued Dec. 23, 1941 to Peck et al, disclosesan early refractor in which lenses in the "weak" lens disc were notmechanically coupled to lenses in the "strong" lens disc. The patentfurther discloses the manner in which the various lens power inindividual discs are combined to provide the resultant power desired bythe practitioner. Although one object of the described invention is toprovide a "cooperatively functioning series of lenses computed as tocurvatures and thicknesses, distance between lenses of said series andposition of said lenses before the eye", the patent contains nodescription of the lens series by or means for determining the lensseries. AMERICAN JOURNAL OF OPTOMETRY AND PHYSIOLOGICAL OPTICS, Volume52, Pages 533-540 (August, 1975) presents a reprint of a paper read atthe American Academy of Optometry Annual Meeting in December of 1974,entitled Additive Lens Systems in Eye Refractors. The paper evaluatesthe lens series of the 1923 Tillyer patent and establishes that theseries is correct for only two lenses in combination. The paper furtherpoints out that additional lenses can cause additive error in excess of0.5 diopter. In conclusion, the paper finds that a programmable desk topcalculator, a computer actuated eye refractor, or a micro computer arerequired to present a plurality of lenses without additive error orconvert the lenses actually presented to real power when printing outthe prescription.

It is an object of the present invention to overcome the deficienciesand inadequacies of the prior art.

It is another object of the present invention to provide a lens seriesfor use in a refractor having predictable combinations of lenses whichproduce significant additive error.

It is still another object of the present invention to provide a lensseries in which additive error of every combination of cylinder lensesis identical for all lenses of the strong sphere dial including the zeropower plate.

BRIEF DESCRIPTION OF THE INVENTION AND DRAWINGS

A refractor singlet lens series, where all lenses presented at thereference plane (called the A lenses) have the same glass or plastic,the same thickness, one surface having the same radius and the samespacings to the next combined lens, will not change the additive errorfor a combination of three or more lenses when the A lens of thecombination is changed. It is understood that, if the series of A lensescontains a zero power position, this position must have a zero powerlens meeting the same requirements as any other A lens. Since the amountof significant additive error remains unchanged in spite of changes inthe A lenses, the number of different corrections in all possible lenscombinations which must be calculated or are required is reduced by afactor equal to the number of A lenses. Although the constant radius ofthe A lenses need not be infinity, a planar surface is preferred sincethe planar surface reduces the problems associated with constructing azero power lens (window) to a minimum. The lenses at the reference planemay be made of either glass or plastic since the critical property isindex of refraction in the composition of the lens material. As long asall lenses have the same index of refraction, they could even be amixture of glass and plastic. Also, lenses other than those at thereference plane can be either glass or plastic.

In a refractor having weak sphere lenses, strong sphere lenses, weakcylinder lenses, and strong cylinder lenses, each respectively carriedby a rotatable dial to permit a selected one of each group of lenses tobe placed before a patient's eye, the preferred embodiment is arrangedwith the strong sphere dial located at the reference plane and has aseries of lenses of identical center thickness, identical glass, and aplanar surface on the side of the lenses furthest from the patient'seye. Such a lens series will provide identical error for eachcombination of cylinder lenses in every position of the strong spheredial.

The radius of the surface closest to the eye must be individuallydetermined for each lens based upon the spacing of the lens from the eyeand the power desired. While not constant, the radii for all lenses in asingle dial will be related, since the spacing thickness and index ofrefraction for all lenses in that dial are identical. The lens series ofthe present invention when incorporated into a refractor reduces theprior art additive cylinder errors in a refractor having 12 positions ofthe strong sphere dial by a factor of 12 and provides 100%predictability of the occurrence of significant additive errors sinceevery position of the strong sphere dial has identical errors.

The drawing is an optical diagram illustrating the position ofrepresentative lenses in a refractor having a lens series of the presentinvention.

DETAILED DESCRIPTION OF THE INVENTION AND PREFERRED EMBODIMENT

Referring to FIG. 1, the lenses in the strong sphere disc of a refractorare identified by I and have variable radius R₁.1 to R₁.12. The lensesin the weak sphere dial are represented by the lens identified by II andhave radii of R₂.1 to R₂.12. Similarly, strong cylinder lenses arerepresented by the lens identified III and have individual radiiidentified as R₃.1 to R₃.12 and weak cylinder lenses represented by thelens identified by IV and have respective radii R₄.1 to R₄.6. Anauxiliary dial in a refractor is frequently used to carry specialoptical elements for conducting certain tests during refraction. Theoptical elements are represented by lens V and preferably include 0.125diopter auxiliary sphere lens. The lenses have radii R₅.1 to R₅.2.Refractors frequently have window VI in order to keep dust and dirt fromthe interior mechanism and optical surfaces. The distance from theoptical surface furthest from the eye of the various elements to thereference plane are identified as D1 to D5 for the weak cylinder lenses,strong cylinder lenses, auxiliary lenses, weak sphere lenses and strongsphere lenses, respectively. The distance from the reference plane tothe window and to the patient's eye are respectively identified as D6and D7. All lenses including the window and auxiliary lens are made of aglass having an index of 1.523, an Abbe number of 58.6 and a thicknessof 1.6 millimeters. The index of refraction of the lenses may be variedby ±0.0005, Abbe number ±0.5 and thickness (except the auxiliary lens)by ±0.2 millimter. While zero power position in the weak sphere, strongcylinder, weak cylinder and auxiliary dials is an open aperture, thestrong sphere disc has a planar plate of the same glass and thickness asthe lenses. This plate has a radius identified as infinity in the table,while zero diopter positions in other discs are noted as having a zeroradius since no glass is present.

Since all lenses have an identical center thickness of 1.6 mm, thespacing between lenses of adjacent dials will be identical regardless ofwhich lens in either dial is positioned before the eye. For the lensseries of the preferred embodiment S1 is 2.368, S2 is 2.877, S3 is 2.368and S4 is 2.368 mm. The distances identified in the drawing areD1=17.981, D2=14.013, D3=9.536, D4=5.568, D6=1.6, D6=1.57, and D7=14.27mm. Table I provides the marked power, real power, calculated radius andactual radius of the variable surface for each lens of respective dialsI-IV and the one lens of auxiliary dial V. Those radii, calculated andactual which are 0.00 identify open apertures in the respective discsdials. The lens having radius R₃.7 has a planar surface on both sides asindicated by the calculated and actual radius of infinity. All the radiiare in millimeters and a minus sign (-) denotes a radius having a centeron the side of the lens away from the patient's eye.

                  TABLE I                                                         ______________________________________                                                                      CALCU-                                          POSI-        MARKED    REAL   LATED    ACTUAL                                 TION  NO.    POWER     POWER  RADIUS   RADIUS                                 ______________________________________                                        STRONG CYLINDRICAL POWERS (DIAL III)                                          1     .sup.R 3.1                                                                           0.0       0.0    0.0      0.0                                    2     3.2    0.750     0.743  703.53797                                                                              703.538                                3     3.3    1.500     1.474  354.87131                                                                              354.871                                4     3.4    2.250     2.192  238.64909                                                                              238.649                                5     3.5    3.000     2.897  180.53797                                                                              180.538                                6     3.6    3.750     3.590  145.67131                                                                              145.671                                7     3.7    4.500     4.272  122.42686                                                                              122.427                                8     3.8    5.250     4.942  105.82369                                                                              105.824                                9     3.9    6.000     5.601  93.37131 93.371                                 10    3.10   6.750     6.250  83.68612 83.686                                 11    3.11   7.500     6.887  75.93797 75.938                                 12    3.12   8.250     7.515  69.59858 69.599                                 WEAK CYLINDRICAL POWERS (DIAL IV)                                             1     .sup.R 4.1                                                                           0.0       0.0    0.0      0.0                                    2     4.2    0.125     0.125  4192.27990                                                                             4192.280                               3     4.3    0.250     0.249  2100.27990                                                                             2100.280                               4     4.4    0.375     0.373  1402.94657                                                                             1402.947                               5     4.5    0.500     0.496  1054.27990                                                                             1054.280                               6     4.6    0.625     0.619  845.07990                                                                              845.080                                STRONG SPHERICAL POWERS (DIAL I)                                              1     .sup.R 1.1                                                                           -18.000   -18.000                                                                              -29.05556                                                                              -29.056                                2     1.2    -15.000   -15.000                                                                              - 34.86667                                                                             -34.867                                3     1.3    -12.000   -12.000                                                                              -43.58333                                                                              -43.583                                4     1.4    -9.000    -9.000 -58.11111                                                                              -58.111                                5     1.5    -6.000    -6.000 -87.16667                                                                              -67.167                                6     1.6    -3.000    -3.000 -174.33333                                                                             -174.333                               7     1.7    0.0       0.000  ∞  ∞                                8     1.8    3.000     3.000  174.33333                                                                              174.333                                9     1.9    6.000     6.000  87.16667 87.167                                 10    1.10   9.000     9.000  58.11111 58.111                                 11    1.11   12.000    12.000 43.58333 43.583                                 12    1.12   15.000    15.000 34.86667 34.867                                 WEAK SPHERICAL POWERS (DIAL II)                                               1     .sup.R 2.1                                                                           -1.000    -1.003 -521.21209                                                                             -521.212                               2     2.2    -0.750    -0.752 -695.54543                                                                             -695.544                               3     2.3    -0.500    -0.501 -1044.21209                                                                            -1044.212                              4     2.4    -0.250    -0.250 -2090.21209                                                                            -2090.212                              5     2.5    0.0       0.0    0.0      0.0                                    6     2.6    0.250     0.250  2093.78791                                                                             2093.788                               7     2.7    0.500     0.499  1047.78791                                                                             1047.788                               8     2.8    0.750     0.748  699.12124                                                                              699.121                                9     2.9    1.000     0.997  524.78791                                                                              524.788                                10    2.10   1.250     1.245  420.18791                                                                              420.188                                11    2.11   1.500     1.492  350.45457                                                                              350.455                                12    2.12   1.750     1.740  300.64505                                                                              300.645                                AUXILIARY SPHERICAL POWERS (DIAL V)                                           1     .sup.R 5.1                                                                           0.0       0.0    0.0      0.0                                    2     5.2    0.125     0.125  4187.86317                                                                             4187.86317                             ______________________________________                                    

A refractor having a lens series with the foregoing values will exhibitdeviation at far point testing (20 ft.) from the marked additive powersonly in those positions shown in Table II. Corrections of +0.125cylinder diopter for these deviations in marked cylinder power are madeby changing the cylinder power for those positions of the weak spheredial presenting a negative sphere power. For example, when the cylinderpower is 8.25; and the weak sphere lens in position 1 of dial II (-1.00diopter) and auxiliary dial V in position 2 (+0.125 diopter) thecorrection would be made by increasing the cylinder power from 8.25 to8.38. Similarly, for those positions of dial II having a spherical powerof 0 or greater, the cylinder power would be reduced by 0.125 diopter.For example, when the cylinder power is 6.63, and the weak sphere lensin position 9 of dial II (+1.00 diopter) and auxiliary dial V inposition 1 (0.0 diopter) are on the test axis, correction would be madeby reducing the cylinder power from 6.63 to 6.50. When the lenscombinations for far point testing are adjusted as indicated above, theerror for any combination of cylinder and spherical lenses is less than+0.10 cylinder diopters. In fact, for those combinations which have beencorrected, the error is reduced to not more than 0.075 diopters. Sincethe errors occurring in any position of the strong sphere dial I are thesame as the errors occurring in any other position of strong sphere dialI, the adjustments which are provided for the zero power position(position 7) of strong sphere dial I are used in all other positions ofthe strong sphere dial.

    TABLE II         STRONG CYL. (III)     01----02----03----04----05----06----07----08----09----10----11----12--     STRONG WEAK  WEAK CYL. (IV) SPHERE (I) SPHERE (II) AUXILIARY (V)     123456123456123456123456123456123456123456123456123456123456123456123456S     PHERE POWER       77777 :::::      11223 ::::: 12121     ##STR1##      77777 :::::      34455 ::::: 21212     ##STR2##      77777 :::::      66778 ::::: 1212 1     ##STR3##      77777 :::::      8991010 ::: :: 21212     ##STR4##      777 7 :::: 11111212 :::: 1212      ##STR5##      CYLINDER POWER   ERROR RANGE (DIOPTERS) SYMBOL      ##STR6##      0.10   E< E ≦ 0.10≦      0.25 BLANK*

Table III presents the error range at near point testing (16 in.) forall combinations of the strong cylinder dial III and weak cylinder dialIV with the weak sphere dial II and auxiliary dial V when the strongsphere dial I is in the zero power position (position 7). As can be seenin Table III, the number combinations having error and the amount oferror in many combinations is substantially larger than the additiveerrors encountered during far point testing.

    TABLE III      STRONG CYL. (III) STRONG  WEAK     01----02----03----04----05----06----07----08----09----10----11----12--     SPHERE  SPHERE    WEAK CYL. (III) (I)  (II)  AUXILIARY (V)  1234561234561     23456123456123456123456123456123456123456123456123456123456SPHERE POWER          77777 :::::  11223 ::::: 12121      ##STR7##      77777 : :::: 34455 ::::: 21212     ##STR8##      77777  ::::: 66778 ::::: 12121     ##STR9##      77777  ::::: 8991010 ::::: 21212     ##STR10##      7777 ::::  11111212 :::: 1212     ##STR11##      ERROR RANGE (DIOPTERS) SYMBOL      ##STR12##      0.100.250.50 <<< EEEE ≦≦≦0.100.250.50 BLANK     *#x

After adjustments, the cylinder error can be reduced to less than atenth of a diopter for all but a few cylinder lens combinations. Thecylinder lens combinations after adjustment are shown in Table IV withthe range of error associated with each combination. Note that only thevery high combinations (over 8.25 diopters of cylinder) result in anyerror for near point because it is not possible to provide the necessarysubstantial increases by adjustment since the maximum cylinder power ofany combination is 8.75. This explains the substantial cylinder error inthe localized region shown by Table IV following adjustment. Table Vprovides the location and type of cylinder power adjustment required foreach combination of cylinder lenses. These adjustment are made for eachcombination which requires adjustment in the same manner as theadjustments described of negative sphere powers for far point testing.

    TABLE IV         STRONG CYL. (III)     01----02----03----04----05----06----07----08----09----10----11----12--     STRONG WEAK  WEAK CYL. (IV) SPHERE (I) SPHERE (II) AUXILIARY (V)     123456123456123456123456123456123456123456123456123456123456123456123456S     PHERE POWER       77777 :::::      11223 ::::: 12121     ##STR13##      77777 :::::      34455 :::::  21212     ##STR14##      77777 :::::      667 78 ::::: 12121     ##STR15##      77777 :::: :      8991010 ::::: 21212     ##STR16##      7777  :::: 11111212 :::: 1212      ##STR17##       ERROR RANGE (DIOPTERS) SYMBOL     ##STR18##      0.10000.11250.1250   E< E< E< E ≦ 0.10≦ 0.1125≦     0.1250 BLANK*#x

    TABLE V         STRONG CYL. (III)     01----02----03----04----05----06----07----08----09----10----11----12--     STRONG WEAK  WEAK CYL. (IV) SPHERE (I) SPHERE (II) AUXILIARY (V)     123456123456123456123456123456123456123456123456123456123456123456123456S     PHERE POWER       77777 :::::      11223 ::::: 12121     ##STR19##      77777 :: :::      34455 ::::: 21212     ##STR20##      77777 :::::      66778 ::::: 12121     ##STR21##      77777 :::::      8991010 ::::: 21212     ##STR22##      7777 :::: 11111212 :::: 1212      ##STR23##        ADJUSTMENT SYMBOL     ##STR24##      AdjustmentLimited By Max.Cylinder Power NONE0.1250.2500.3750.500        3    4     BLANK12

Table VI is representative of the amount of cylinder error, at nearpoint, and shows the precise amount of spherical and cylinder error foreach combination of the weak cylinder dial IV with the strong cylinderdial III when the spherical power is zero.

Table VII presents the amount of cylinder error for several cylinderpowers and varying positions of strong sphere dial I. Note that whilethe amount of error varies with various cylinder powers, the errorremains identical through the entire range from -18 to +15.250 dioptersof sphere for that cylinder power so long as the weak sphere dial IIand/or auxiliary dial V are not changed.

    __________________________________________________________________________    DIAL AND POSITION                                                             W   S   A   W   S MARKED    ERROR                                             C   C   S   S   S SPHERE                                                                              CYL.                                                                              SPHERE                                                                              CYL.                                        __________________________________________________________________________    1 :  1                                                                              : 1 : 5 :  7                                                                              0.0   0.0 -0.003                                                                              0.0                                         2 :  1                                                                              : 1 : 5 :  7                                                                              0.0   0.125                                                                             -0.007                                                                              -0.010                                      3 :  1                                                                              : 1 : 5 :  7                                                                              0.0   0.250                                                                             -0.007                                                                              -0.019                                      4 :  1                                                                              : 1 : 5 :  7                                                                              0.0   0.375                                                                             -0.007                                                                              -0.029                                      5 :  1                                                                              : 1 : 5 :  7                                                                              0.0   0.500                                                                             -0.007                                                                              -0.038                                      6 :  1                                                                              : 1 : 5 :  7                                                                              0.0   0.625                                                                             -0.007                                                                              -0.048                                      1 :  2                                                                              : 1 : 5 :  7                                                                              0.0   0.750                                                                             -0.007                                                                              -0.043                                      2 :  2                                                                              : 1 : 5 :  7                                                                              0.0   0.875                                                                             -0.010                                                                              -0.051                                      3 :  2                                                                              : 1 : 5 :  7                                                                              0.0   1.000                                                                             -0.010                                                                              -0.058                                      4 :  2                                                                              : 1 : 5 :  7                                                                              0.0   1.125                                                                             -0.010                                                                              -0.065                                      5 :  2                                                                              : 1 : 5 :  7                                                                              0.0   1.250                                                                             -0.010                                                                              -0.073                                      6 :  2                                                                              : 1 : 5 :  7                                                                              0.0   1.375                                                                             -0.010                                                                              -0.080                                      1 :  3                                                                              : 1 : 5 :  7                                                                              0.0   1.500                                                                             -0.007                                                                              -0.087                                      2 :  3                                                                              : 1 : 5 :  7                                                                              0.0   1.625                                                                             -0.010                                                                              -0.093                                      3 :  3                                                                              : 1 : 5 :  7                                                                              0.0   1.750                                                                             -0.010                                                                              -0.098                                      4 :  3                                                                              : 1 : 5 :  7                                                                              0.0   1.875                                                                             -0.010                                                                              -0.103                                      5 :  3                                                                              : 1 : 5 :  7                                                                              0.0   2.000                                                                             -0.010                                                                              -0.109                                      6 :  3                                                                              : 1 : 5 :  7                                                                              0.0   2.125                                                                             -0.010                                                                              -0.114                                      1 :  4                                                                              : 1 : 5 :  7                                                                              0.0   2.250                                                                             -0.007                                                                              -0.131                                      2 :  4                                                                              : 1 : 5 :  7                                                                              0.0   2.375                                                                             -0.010                                                                              -0.135                                      3 :  4                                                                              : 1 : 5 :  7                                                                              0.0   2.500                                                                             -0.010                                                                              -0.138                                      4 :  4                                                                              : 1 : 5 :  7                                                                              0.0   2.625                                                                             -0.010                                                                              -0.141                                      5 :  4                                                                              : 1 : 5 :  7                                                                              0.0   2.750                                                                             -0.010                                                                              -0.145                                      6 :  4                                                                              : 1 : 5 :  7                                                                              0.0   2.875                                                                             -0.010                                                                              -0.148                                      1 :  5                                                                              : 1 : 5 :  7                                                                              0.0   3.000                                                                             -0.007                                                                              -0.176                                      2 :  5                                                                              : 1 : 5 :  7                                                                              0.0   3.125                                                                             -0.010                                                                              -0.177                                      3 :  5                                                                              : 1 : 5 :  7                                                                              0.0   3.250                                                                             -0.010                                                                              -0.179                                      4 :  5                                                                              : 1 : 5 :  7                                                                              0.0   3.375                                                                             -0.010                                                                              -0.180                                      5 :  5                                                                              : 1 : 5 :  7                                                                              0.0   3.500                                                                             -0.010                                                                              -0.181                                      6 :  5                                                                              : 1 : 5 :  7                                                                              0.0   3.625                                                                             -0.010                                                                              -0.182                                      1 :  6                                                                              : 1 : 5 :  7                                                                              0.0   3.750                                                                             -0.007                                                                              -0.221                                      2 :  6                                                                              : 1 : 5 :  7                                                                              0.0   3.875                                                                             -0.010                                                                              -0.220                                      3 :  6                                                                              : 1 : 5 :  7                                                                              0.0   4.000                                                                             -0.010                                                                              -0.219                                      4 :  6                                                                              : 1 : 5 :  7                                                                              0.0   4.125                                                                             -0.010                                                                              -0.218                                      5 :  6                                                                              : 1 : 5 :  7                                                                              0.0   4.250                                                                             -0.010                                                                              -0.218                                      6 :  6                                                                              : 1 : 5 :  7                                                                              0.0   4.375                                                                             -0.010                                                                              -0.217                                      1 :  7                                                                              : 1 : 5 :  7                                                                              0.0   4.500                                                                             -0.007                                                                              -0.266                                      2 :  7                                                                              : 1 : 5 :  7                                                                              0.0   4.625                                                                             -0.010                                                                              -0.264                                      3 :  7                                                                              : 1 : 5 :  7                                                                              0.0   4.750                                                                             -0.010                                                                              -0.261                                      4 :  7                                                                              : 1 : 5 :  7                                                                              0.0   4.875                                                                             -0.010                                                                              -0.258                                      5 :  7                                                                              : 1 : 5 :  7                                                                              0.0   5.000                                                                             -0.010                                                                              -0.255                                      6 :  7                                                                              : 1 : 5 :  7                                                                              0.0   5.125                                                                             -0.010                                                                              -0.252                                      1 :  8                                                                              : 1 : 5 :  7                                                                              0.0   5.250                                                                             -0.007                                                                              -0.312                                      2 :  8                                                                              : 1 : 5 :  7                                                                              0.0   5.375                                                                             -0.010                                                                              -0.307                                      3 :  8                                                                              : 1 : 5 :  7                                                                              0.0   5.500                                                                             -0.010                                                                              -0.302                                      4 :  8                                                                              : 1 : 5 :  7                                                                              0.0   5.625                                                                             -0.010                                                                              -0.297                                      5 :  8                                                                              : 1 : 5 :  7                                                                              0.0   5.750                                                                             -0.010                                                                              -0.292                                      6 :  8                                                                              : 1 : 5 :  7                                                                              0.0   5.875                                                                             -0.010                                                                              -0.287                                      1 :  9                                                                              : 1 : 5 :  7                                                                              0.0   6.000                                                                             -0.007                                                                              -0.358                                      2 :  9                                                                              : 1 : 5 :  7                                                                              0.0   6.125                                                                             -0.010                                                                              -0.351                                      3 :  9                                                                              : 1 : 5 :  7                                                                              0.0   6.250                                                                             -0.010                                                                              -0.344                                      4 :  9                                                                              : 1 : 5 :  7                                                                              0.0   6.375                                                                             -0.010                                                                              -0.337                                      5 :  9                                                                              : 1 : 5 :  7                                                                              0.0   6.500                                                                             -0.010                                                                              -0.329                                      6 :  9                                                                              : 1 : 5 :  7                                                                              0.0   6.625                                                                             -0.010                                                                              -0.322                                      1 : 10                                                                              : 1 : 5 :   7                                                                             0.0   6.750                                                                             -0.007                                                                              -0.404                                      2 : 10                                                                              : 1 : 5 :  7                                                                              0.0   6.875                                                                             -0.010                                                                              -0.395                                      3 : 10                                                                              : 1 : 5 :  7                                                                              0.0   7.000                                                                             -0.010                                                                              -0.386                                      4 : 10                                                                              : 1 : 5 :  7                                                                              0.0   7.125                                                                             -0.010                                                                              -0.377                                      5 : 10                                                                              : 1 : 5 :  7                                                                              0.0   7.250                                                                             -0.010                                                                              -0.367                                      6 : 10                                                                              : 1 : 5 :  7                                                                              0.0   7.375                                                                             -0.010                                                                              -0.385                                      1 : 11                                                                              : 1 : 5 :  7                                                                              0.0   7.500                                                                             -0.007                                                                              -0.451                                      2 : 11                                                                              : 1 : 5 :  7                                                                              0.0   7.625                                                                             -0.010                                                                              -0.440                                      3 : 11                                                                              : 1 : 5 :  7                                                                              0.0   7.750                                                                             -0.010                                                                              -0.429                                      4 : 11                                                                              : 1 : 5 :  7                                                                              0.0   7.875                                                                             -0.010                                                                              -0.417                                      5 : 11                                                                              : 1 : 5 :  7                                                                              0.0   8.000                                                                             -0.010                                                                              -0.405                                      6 : 11                                                                              : 1 : 5 :  7                                                                              0.0   8.125                                                                             -0.010                                                                              -0.394                                      1 : 12                                                                              : 1 : 5 :  7                                                                              0.0   8.250                                                                             -0.007                                                                              -0.498                                      2 : 12                                                                              : 1 : 5 :  7                                                                              0.0   8.375                                                                             -0.010                                                                              -0.485                                      3 : 12                                                                              : 1 : 5 :  7                                                                              0.0   8.500                                                                             -0.010                                                                              -0.471                                      4 : 12                                                                              : 1 : 5 :  7                                                                              0.0   8.625                                                                             -0.010                                                                              -0.458                                      5 : 12                                                                              : 1 : 5 :  7                                                                              0.0   8.750                                                                             -0.010                                                                              -0.444                                      6 : 12                                                                              : 1 : 5 :  7                                                                              0.0   8.875                                                                             -0.010                                                                              -0.430                                      IV  III V   II  I                                                             1 :  9                                                                              : 1 : 6 :  1                                                                              -17.750                                                                             6.000     -0.350                                      1 :  9                                                                              : 1 : 6 :  4                                                                              -8.750                                                                              6.000     -0.350                                      1 :  9                                                                              : 1 : 6 :  7                                                                              0.250 6.000     -0.350                                      1 :  9                                                                              : 1 : 6 : 10                                                                              9.250 6.000     -0.350                                      1 :  9                                                                              : 1 : 6 : 12                                                                              15.250                                                                              6.000     -0.350                                      1 :  9                                                                              : 1 : 5 :  1                                                                              -18.000                                                                             6.000     -0.358                                      1 :  9                                                                              : 1 : 5 :  4                                                                              -9.000                                                                              6.000     -0.358                                      1 :  9                                                                              : 1 : 5 :  7                                                                              0.000 6.000     -0.358                                      1 :  9                                                                              : 1 : 5 : 10                                                                              9.000 6.000     -0.358                                      1 :  9                                                                              : 1 : 5 : 12                                                                              15.000                                                                              6.000     -0.358                                      5 : 11                                                                              : 1 : 5 :  1                                                                              -18.000                                                                             8.000     -0.405                                      5 : 11                                                                              : 1 : 5 :  4                                                                              -9.000                                                                              8.000     -0.405                                      5 : 11                                                                              : 1 : 5 :  7                                                                              0.000 8.000     -0.405                                      5 : 11                                                                              : 1 : 5 : 10                                                                              9.000 8.000     -0.405                                      5 : 11                                                                              : 1 : 5 : 12                                                                              15.000                                                                              8.000     -0.405                                      6 : 12                                                                              : 1 : 5 :  1                                                                              -18.000                                                                             8.875     -0.430                                      6 : 12                                                                              : 1 : 5 :  4                                                                              -9.000                                                                              8.875     -0.430                                      6 : 12                                                                              : 1 : 5 :  7                                                                              0.000 8.875     -0.430                                      6 : 12                                                                              : 1 : 5 : 10                                                                              9.000 8.875     -0.430                                      6 : 12                                                                              : 1 : 5 : 12                                                                              15.000                                                                              8.875     -0.430                                      __________________________________________________________________________

Obviously, if one elected to place the strong cylinder lenses in thedial positioned at the referenced plane (A lenses) then the additiveerror of the system would be spherical and cylinder powers would notrequire correction.

Since only two charts, one for distance and one for near, would berequired to identify the positions and the amount of adjustment requiredfor a refractor having a lens series according to the present invention,it would be possible for the practitioner to refer to the chart andmanually make the adjustment. However, because the combination of lenseshaving refractive errors is now 100% predictable, large computers (microcomputer and the like) or programmable desk calculating machines are nolonger necessary to correct for additive error. In fact, it is nowfeasible to utilize a microprocessor since the positions requiringcorrection have been reduced by factor of 12 according to the preferredembodiment.

Refractors commonly have gear means for rotating all cylinder lenses,whether on the test axis or not, during examination. It may beconvenient to mold the peripheral gear conventionally used as anintegral part of each cylinder lens. This may be convenientlyaccomplished by using a polycarbonate resin. The following table setsforth the calculating radii for cylinder lenses (dials III and IV)molded of a polycarbonate resin having an index of refraction of 1.5842.

                  TABLE I                                                         ______________________________________                                                           MARKED    CALCULATED                                       POSITION  NO.      POWER     RADIUS                                           ______________________________________                                        STRONG CYLINDRICAL POWERS (DIAL III)                                          1         .sup.R 3.1                                                                             0.0       0.0                                              2         3.2      0.750     785.86402                                        3         3.3      1.500     396.39736                                        4         3.4      2.250     266.57514                                        5         3.5      3.000     201.66402                                        6         3.6      3.750     162.71736                                        7         3.7      4.500     136.75291                                        8         3.8      5.250     118.20688                                        9         3.9      6.000     104.29736                                        10        3.10     6.750     93.47884                                         11        3.11     7.500     84.82402                                         12        3.12     8.250     77.74281                                         WEAK CYLINDRICAL POWERS (DIAL IV)                                             1         .sup.R 4.1                                                                             0.0       0.0                                              2         4.2      0.125     4682.84879                                       3         4.3      0.250     2346.04879                                       4         4.4      0.375     1567.11546                                       5         4.5      0.500     1177.64879                                       6         4.6      0.625     943.96879                                        ______________________________________                                    

What is claimed is:
 1. A lens series for a refractor having a pluralityof lenses positionable at each of more than two positions spaced alongan optical axis and a reference plane at one of the positions whichcomprises, the plurality of lenses being positionable at the referenceplane including a zero power lens having the same index of refraction,having the same thickness, having the same radius on one surface and thesame distance to other lenses on the optical axis.
 2. A lens seriesaccording to claim 1 wherein at least some of the lenses are plastic. 3.The lens series of claim 2 wherein the plastic is polycarbonate.